Math Problem Statement
show that To determine the stability of a fixed point, we have to linearize Eq. \dot{a} = -i\nu a + a - |a|^2 a - i e, which leads to the characteristic equation λ2 + (4R2 − 2)λ + (1 − 3R2)(1 − R2) + ν2 = 0.
Solution
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Math Problem Analysis
Mathematical Concepts
Dynamical Systems
Linearization
Stability Analysis
Complex Numbers
Formulas
\dot{a} = -i\nu a + a - |a|^2 a - i e
Characteristic equation: λ^2 + (4R^2 − 2)λ + (1 − 3R^2)(1 − R^2) + ν^2 = 0
Theorems
Stability of Fixed Points
Linearization Theorem
Suitable Grade Level
Undergraduate - Advanced Mathematics
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